Review Questions for Midterm

# Review Questions for Midterm - What is Taylor series...

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What is Taylor series expansion in 1-D and 2-D? What is the truncation error in the Taylor series expansion? What does that tell us? What is truncation error in approximating various derivatives using forward difference, backward difference and central difference? How is a floating number represented in a computer? What is the mantissa? Given x= ± . d 1 d 2 d 3 ... d p * B e , -E min e E max , how do you determine the largest possible value for x? What is the machine epsilon? What are the overflow and underflow? What is roundoff error? What are the major difference between chopping and rounding? How does truncation error and roundoff error interact in a computation? How to define error and relative error? How does error propagate in addition/subtraction, multiplication/division, and function evaluation? What is the main idea in bisection method for root finding? How to implement it? What is the rate of convergence or how does the error decrease during iteration?

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